Question: Which of the following numbers is a factor of 112? ${4,6,9,10,11}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $112$ by each of our answer choices. $112 \div 4 = 28$ $112 \div 6 = 18\text{ R }4$ $112 \div 9 = 12\text{ R }4$ $112 \div 10 = 11\text{ R }2$ $112 \div 11 = 10\text{ R }2$ The only answer choice that divides into $112$ with no remainder is $4$ $ 28$ $4$ $112$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $112$ $112 = 2\times2\times2\times2\times7 4 = 2\times2$ Therefore the only factor of $112$ out of our choices is $4$. We can say that $112$ is divisible by $4$.